To determine whether the situation represents a linear or non-linear function, we can analyze the changes in the number of math problems completed as the minutes increase.
Let's look at the data more closely:
- From 1 minute to 2 minutes: \(7 - 3 = 4\) problems
- From 2 minutes to 3 minutes: \(12 - 7 = 5\) problems
- From 3 minutes to 4 minutes: \(16 - 12 = 4\) problems
- From 4 minutes to 5 minutes: \(19 - 16 = 3\) problems
Now, we see how the number of problems completed changes over time:
- The change in problems over the first interval (1 to 2 minutes) is 4.
- The change over the second interval (2 to 3 minutes) is 5.
- The change over the third interval (3 to 4 minutes) is 4.
- The change over the fourth interval (4 to 5 minutes) is 3.
Since the differences in the number of problems completed are not constant, it indicates that Jana's completion of math problems does not follow a linear relationship.
Based on this analysis, the correct answer is:
It represents a non-linear function because there is not a constant rate of change.
2 answers